The connection between $P$-fractions and associated fractions
Author:
Arne Magnus
Journal:
Proc. Amer. Math. Soc. 25 (1970), 676-679
MSC:
Primary 40.12
DOI:
https://doi.org/10.1090/S0002-9939-1970-0259412-2
MathSciNet review:
0259412
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Abstract | References | Similar Articles | Additional Information
Abstract: The associated continued fractions of a power series $L$ is a special case of the $P$-fraction of a power series ${L^{\ast }}$. The latter is closely connected with the Padé table of ${L^{\ast }}$. We prove that every $P$-fraction is the limit of the appropriate contraction of associated fractions in the sense that as the coefficients of $L$ approach those of ${L^{\ast }}$ the elements and approximants of the contraction approach the elements and approximants of the $P$-fraction.
- Oskar Perron, Die Lehre von den Kettenbrüchen. Dritte, verbesserte und erweiterte Aufl. Bd. II. Analytisch-funktionentheoretische Kettenbrüche, B. G. Teubner Verlagsgesellschaft, Stuttgart, 1957 (German). MR 0085349
- Arne Magnus, Certain continued fractions associated with the Padé table, Math. Z. 78 (1962), 361–374. MR 150271, DOI https://doi.org/10.1007/BF01195180
- Arne Magnus, Expansion of power series into $P$-fractions, Math. Z. 80 (1962), 209–216. MR 150272, DOI https://doi.org/10.1007/BF01162378
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Keywords:
Continued fractions,
associated continued fractions,
<IMG WIDTH="21" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$P$">-fractions,
Padé table
Article copyright:
© Copyright 1970
American Mathematical Society